As soon as a bowling ball rolls off the edge of a table its horizontal component of velocity

It will remain constant

Explanation:

The motion of the bowling ball, after it rolls off the table, is the motion of a projectile, which consists of two independent motions:

- A uniform motion (constant velocity) along the horizontal direction

- An accelerated motion (with constant downward acceleration, g=9.8 m/s^2) along the vertical direction

We are only interested in the horizontal motion: there are no forces acting along the horizontal direction (if we neglect air resistance), this means that the horizontal acceleration is zero, and therefore the horizontal component of the velocity of the ball will remain constant.